What is the equation of the line with x-intercept 5 and y-intercept equal to 8?

Expert Answers
hala718 eNotes educator| Certified Educator

We know that the x-intercept =5 Then the line passes through the point (5,0)

Also we know that the y-intercept= 8, then the line passes through the point (0,8)

Now we have 2 points pass through the line, then we can calculate the slope (m)

m= (y2-y1)/(x2-x1)= -8/5

Then the equation is:

y-y1=m(x-x1)

y-8= (-8/5)(x-0)

y= (-8/5)x + 8

giorgiana1976 | Student

To find the equation of the line which intersects the axis x and y, we'll find the coordinates of the intersection points.

When the line is intercepting the x axis, the coordinate for x is 5 and for y is 0, so the first intersection point is P1(5,0).

When the line is intercepting the y axis, the coordinate for x is 0 and for y is 8, so the second intersection point is P2(0,8).

Now, we'll write the equation of the line which passes through the points P1 and P2.

(xP2 - xP1)/(x -xP1) = (yP2 - yP1)/(y - yP1)

We'll substitute the coordinates for P1 and P2:

(0-5)/(x-5) = (8-0)/(y-0)

-5/(x-5) = 8/y

We'll cross multiplying:

-5y = 8x - 40

We'll divide by -5 both sides:

y = -8x/5 + 8

The equation of the line which intersects x and y axis is:

y = -8x/5 + 8